It's a long flight but go to the SOTHIS system and pick up only data missions from the Federation broker which will be indicated by the Federation watermark next to him or her. And then go to all the available stations in the system and do the same, be careful not to work for any other broker, only the Federation broker. All the data mission will go one jump to various stations in the system CEOS. As you drop off the current data missions, pick up available new ones from the Federation broker just as you did in SOTHIS. All of the mission you pick up will go to the various stations in SOTHIS. Repeat over and over and over again until you've reached the rank you wish to stop at. Generally the REAR ADMIRAL rank, as the Corvette lock becomes available at that level of rank. Presently, there's no reason to proceed to Admiral, but some as myself do it just because.
Ranking up in regards to the EMPIRE can be done much in the same way, but involves two other systems.
Suggestion would be to buy a Python, with no weapons nor utilities, fill the optional slots with nothing but eco cabins except for a size 3 generator, using coralis web site, click on the icon next to the top of the cores labled core internal and choose maximum jump range. Install the suggestion.
Remove the largest passenger cabin and place it in storage, replace it with a "A" graded fuel scoop. Fly ALL the way to ROBIGO and land at ROBIGO MINES. Have your cabin shipped to you and stow your scoop to be used for the trip back when your done. Pickup any and all mission going to Sirius Atmospherics located near planet A5 in SOTHIS. Scan the beacon and return to Robigo Mines. You will make millions and millions and more millions, or if you choose, you can make rep until your allied, then switch to inf. In which case you'll still make a bit of money, but all the influnce will be attributed your federation rank progress.
If and when you've got to your first billion. You'll have enough federal influence saved up that when you go to SOTHIS to start the ranking up process as I described. You can make it all the way to at least LT Cmdr. extremely quick. The influene indicator will seem to stop at 100 percent, but rest assurd that there is considerably more.
Though some think it's an exploit and cheating, some don't, play how you want.